wrist, has it been continually sore for years or just worse now since this shoulder injury?
good thatdr checked for obvious instability - it may be acive instability, ie when you are using your arm at extremes, such as rows that cause problem rather than just when at rest in the drs office.
my opinion, US scan and inject under guidance into what they see at time and not do blind.
yes definetly see a physio!
good luck